Test method for surface figure of large convex mirrors

ABSTRACT

A method of testing a convex mirror surface figure in which an optical quality substrate material is used having a convex front surface and a rear surface polished to a precise optical figure to create a lens. The lens is then tested by a standard interferometric or wavefront lens-testing method and the convex surface coated once a desired curvature is obtained. Null testing may be attained by passing a collimated interferometer beam through a focusing lens shaped to counter the predicted spherical aberration introduced by a perfect convex mirror/lens.

BACKGROUND

The invention relates generally to a method of testing the surface quality of convex mirrors, and, in particular, to using an optical lens quality material as the mirror substrate, polishing the rear surface of the substrate to a precise surface figure to thereby transform it into a lens, and testing this lens by standard interferometric or wavefront methods prior to applying a reflective coating to the convex surface.

Large convex mirrors are typically used as secondary mirrors in large reflecting telescopes. For example, the NASA 3-meter telescope on Mona Kea uses a 244-mm diameter secondary mirror having a hyperbolic surface figure. Currently the standard method for testing convex mirrors is the Hindle sphere test or the improved version, the Hindle-Simpson test. The Hindle test uses a spherical mirror that is significantly larger in diameter than the convex mirror under test and it must be perforated at its center. A diagram of the test set-up is shown in FIG. 1.

The convex mirror under test, the test optic 10, is tested at the same conjugates as used in the telescope by employing a Hindle Sphere 11, a spherical mirror with a central perforation. The center of curvature (CoC) of the Hindle Sphere is positioned at the near focus 12 of the convex surface under test. The diameter of the Hindle Sphere has to be greater than that of the test optic. Light from an interferometer 13 is brought to the null test point 14 at the far focus of the convex surface of the test optic. After reflections off the test optic 10 and the Hindle Sphere 11, the light re-traces its path back to the interferometer 13 where it produces fringes on a monitor 15 depicting the wavefront aberrations of the test optic.

A schematic of the Hindle-Simpson test set-up is shown in FIG. 2. This test makes use of a meniscus-shaped Hindle Sphere 20 and a concave calibration mirror 21. All surfaces in the arrangement are spherical. By designing the ancillary optics, in this case the meniscus-shaped Hindle Sphere and the concave calibration mirror, to lie close to the convex mirror under test 22, the diameters of these optics are minimized with corresponding reduction in cost of fabrication. Nonetheless, the diameters still have to be somewhat larger than the diameter of the test optic.

In large telescopes, astronomical or otherwise, the secondary mirror often directs the light to a focus through a central hole in the primary. The distance from the vertex of the secondary mirror to this focus can be many meters, perhaps more than 10 meters. To reduce the total length of the test setup, a shortening lens 30 is often used as shown in FIG. 3. The lens is often a plano-convex lens with spherical convex surface. Again, this lens has to have a diameter greater than the diameter of the mirror under test 31, further adding to the complexity and cost of the test setup.

There is a need for a less complex and less expensive method of testing the surface of a convex mirror to enable accurate measurement and characterization of its surface figure.

SUMMARY

A new method of testing the surface figure of a convex mirror is presented that allows a significant reduction in the complexity and size of the ancillary test optics, making their fabrication simpler and less expensive. In a preferred embodiment the convex mirror under test is first fabricated from a substrate material that is transmissive at the chosen test wavelength and has good optical homogeneity. The rear of the mirror is polished and figured to some convenient shape so that the mirror can now be tested as though it were a lens. The mirror, which may now be refer to as a “Mirror/Lens”, can then be null tested at convenient conjugates that are not necessarily the same as those used by the mirror in its designed application. The combination of these three features potentially allows the ancillary optics to be constructed to a higher optical precision, which ultimately translates to more precise testing and characterization of the convex mirror surface under test.

Other aspects and advantages of the present invention will become apparent from the following detailed description, taken in conjunction with the accompanying drawings, illustrating by way of example the principles of the invention.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic of the Hindle sphere test set-up for testing a convex mirror.

FIG. 2 is a schematic of the Hindle-Simpson sphere test set-up.

FIG. 3 shows the Hindle-Simpson test schematic where a shortening lens is used to reduce the total path length and produce a more compact arrangement.

FIG. 4 is a schematic of an interferometric test configuration for testing the surface figure of a convex mirror/lens as per the present invention.

FIG. 5 is a schematic for testing the secondary mirror of the NASA 3-meter telescope offered as one example of the present invention.

FIG. 6 is a plot of the residual wavefront aberration for a perfectly figured mirror/lens surface set up in double-pass as in FIG. 5.

FIG. 7A shows the fringe pattern for a perfectly figured Mirror/Lens showing residual wavefront aberrations obtained from FIG. 5 test setup.

FIG. 7B shows the same fringe pattern as in FIG. 7A with wavefront error magnified 50× to show the otherwise imperceptible fringe-shape details.

FIG. 8 shows a simple test set-up using an interferometer equipped with a transmission sphere.

DESCRIPTION OF THE PREFERRED EMBODIMENT

Current methods of testing the surface quality of convex mirrors involve ancillary optics that are significant larger than the mirror under test. For secondary mirrors used in large telescopes, the test set-ups are quite large since the same conjugates are used as in the actual telescope. The present invention results in a significant reduction in the size and complexity of the ancillary test optics, making the fabrication and assembly of these optics simpler and less expensive and enabling greater optical precision.

To act as a lens, the substrate of the convex mirror under test has to be made from transmissive material. There are many types of glass, plastic, crystalline, and other materials from which to choose. Zerodur or fused silica might often be used because of their low thermal expansion coefficients. The material would have to have good optical homogeneity so that the substrate itself does not introduce significant wavefront aberrations.

The substrate material of convex mirrors are normally ground and polished to the required curvature and then coated with a reflective material. In the present invention, the substrate material of the mirror is fabricated from a material that transmits light at the chosen test wavelength and has good optical homogeneity. The front side of the substrate is shaped and polished to approximately the desired convex curvature. The rear side of the substrate is also shaped to a precise surface figure, thereby transforming the substrate into a lens. The simplest rear surface figure would be an optical flat. However, this surface could be any other spherical or aspheric, convex or concave shape, depending on how the test is configured. Iteratively testing and polishing the test optic until a desired convex surface quality is obtained may then be carried out using a standard interferometric or wavefront lens-testing method. Once the desired convex surface is obtained, the surface is coated with a reflective material to thereby produce the desired convex mirror.

The surface figure of this mirror/lens, referred to as the test optic, may also be tested at convenient imaging conjugates that are not necessarily the same as those used by the mirror in its final application, enabling much simpler and more compact geometries. FIG. 4 shows a schematic of one test arrangement in which a standard interferometer transmits a collimated beam 40 through a focusing lens 41. The focusing lens initially converges the beam to a spot 42. The beam then diverges. The test optic 43 is located at a point where the diverging beam fills the test optic lens. The beam passes through the test optic and is reflected back through the test optic by a return mirror 44. It then passes through the focusing lens and creates a fringe pattern (not shown) determined by the irregularities in the convex surface under test. The two ancillary optics, focusing lens 41 and return mirror 44, may now be much smaller than the test optic. The rear surface of the test optic 45 may be flat, concave or convex, spherical or aspheric, depending on the configuration and shape of the return mirror used.

Flat surfaces would normally be preferred over curved ones for cost reasons, consistent with achieving satisfactory performance from the ancillary optics. The next choice would be spherical surfaces, concave or convex. Although aspheric ancillary optics surfaces are also envisaged, they would only be used if there were clear benefit, such as improving the accuracy of the test.

As an example, the testing method was applied to the 244-mm diameter secondary mirror of the NASA 3-meter telescope as shown in FIG. 5. The requirement for this mirror is that, when combined with the 3-meter telescope primary mirror, diffraction limited performance is delivered (<λ/4 HeNe). Prior knowledge of the surface figure of the 3-meter primary mirror had previously been established by measurement. Based on this knowledge, NASA deemed that the ideal secondary mirror prescription is as follows:

Substrate material: Zerodur

Diameter: 244 mm

Radius of curvature: 1311.6 mm

Conic constant: k=−1.2068

Vertex thickness: 19.304 mm

As setup in FIG. 5, the aspheric surface 50 of the mirror/lens (test optic) is chosen facing the return flat 51, a choice that leads to significantly reduced complexity of the ancillary optics. For testing other types of convex mirrors, the test optic could of course be reversed to face the other direction. In designing the test setup for this mirror, the preferred objective is to create a null test. In a null test, the ancillary optics are arranged such that a perfectly figured mirror under test would produce a null fringe pattern. A further objective is to make the ancillary tests optics as small, simple and inexpensive as possible, consistent with achieving the required test accuracy.

Although a flat return mirror 51 is shown in FIG. 5, in general there is no need to restrict to flat surfaces. If the return mirror were concave or convex spherical as in FIG. 4, its diameter could then be significantly smaller than the diameter of the test optic.

The layout shown in FIG. 5 comprises (on the right) a plano-convex spherical focusing lens 62 with the following specifications:

Substrate material: Fused silica

Lens type: Plano-convex (spherical)

Diameter: ˜60 mm

Clear Aperture (CA) diameter: 50.8 mm

Radius of curvature: 391 mm

Vertex thickness: 15 mm

The actual diameter of the focusing lens is chosen larger than the 50.8-mm CA diameter to ensure good optical figure over CA. The lens brings the collimated beam 53 from the interferometer to a focused spot 54 at distance of 506 mm. The beam then diverges over a further 2421-mm path to fill the 244-mm diameter Mirror/Lens under test. As shown, the distance from the focused spot to the Mirror/Lens is exactly the same as the focal length of the Mirror/Lens. As a result, the Mirror/Lens collimates the light towards the 244-mm diameter return flat 51. After reflecting from the return flat, the beam retraces its path back into the interferometer where it produces fringe patterns (not shown) representing the figure errors of the Mirror/Lens surface under test.

Set up as in FIG. 5, the test optic introduces a significant amount of spherical aberration. The plano-convex-spherical focusing lens 52 is therefore designed to introduce an equal and opposite amount of spherical aberration. The degree of compensation achieved in the double-pass arrangement shown in FIG. 5 is such that the test constitutes a null test to high accuracy. Residual (uncorrected) wavefront error is less than λ/120 (HeNe). Consequently, whereas the convex surface under test in FIG. 5 is not tested at its natural null points, as it would with the Hindle Sphere test, the test is nonetheless a null test in every other sense.

Expanding on this, if the 244-mm diameter secondary test optic were to have the ideal, perfectly figured aspheric surface (radius of curvature 1311.6 mm, and conic constant −1.2068) and the rear surface were perfectly flat, and the return mirror were also perfectly flat, and the plano-convex-spherical lens surfaces were also perfectly figured, the residual double-pass wavefront aberration would be less than λ/120 (HeNe) as shown in FIG. 6.

The fringe pattern corresponding to the FIG. 6 double-pass wavefront aberration is shown in FIG. 7A. FIG. 7B is a 50× magnified view of the FIG. 7A fringes. The fringes in FIG. 7A look almost perfectly straight indicating an extremely well figured test optic convex surface. Of course, by use of more sophisticated ancillary optics, residual wavefront aberration could be reduced further, or eliminated altogether, so that a true null fringe pattern could be obtained.

If an interferometer producing the collimated beam 81 is equipped with a transmission sphere 82, in principle, the only additional requirement to test a convex mirror 83 would be to polish the rear surface flat 84 so that this surface acts as the return flat. Such an arrangement is shown in FIG. 8.

Generally, the transmission reference sphere does not compensate for spherical aberration generated by the double-pass through test optic Transmission spheres generally provide near-perfect spherical wavefronts entirely free of any sort of spherical aberration. Therefore, it is not usually possible to use the FIG. 8 arrangement as a null test. Tested as in FIG. 8, a perfectly figured convex surface of the test optic would produce a non-zero but predicable wavefront error. If predicted wavefront error data were subtracted from the measured fringe pattern, a pseudo-null fringe pattern would result.

Interpretation of Fringe Patterns and Assessment of Surface Figure Error

For a mirror surface tested in reflection, a surface height error, H, produces wavefront error, W, as follows: W=2H  (1)

When the same surface is tested in transmission, as in a lens, exactly the same surface height error, H, gives rise to wavefront error, W, given by W=(n−1)H  (2) where n is the refractive index of the substrate material used to make the mirror.

For many types of glass, n is about 1.5 but other glass types have refractive indices greater than 2. For crystalline substrates, n may be even higher. For Zerodur, as used in the FIG. 5 setup, n=1.54 at HeNe (633 nm). Equation (2) then becomes W=0.54H  (3)

In the FIG. 5 test, the beam passes through the fused silica Mirror/Lens twice. In this case the wavefront error is given by W=2.(n−1)H=1.08H  (4)

Comparison of Equations (1) and (4) indicates that the test method described in this disclosure is about 2 times less sensitive than is the case when mirrors are tested in reflection. To illustrate the difference, for a 1-micron surface height irregularity, under the standard test in reflection described by Equation (1), we should expect to see 2H/λ≈3.2 fringes (HeNe). Under the Mirror/Lens test (Equation 4) we should expect to see 1.08H/λ≈1.75 fringes (HeNe).

With the Hindle Sphere test illustrated in FIG. 1, the beam two reflections off the convex mirror under test. For this case, wavefront aberration, W, is given by W=4H  (5)

The test sensitivity of the present invention is about 1.85× less than that of a standard mirror interferometric test where there is a single-reflection (c.f. Equations 1 and 4). The test sensitivity of the present invention is about a 3.7× less than that of a Hindle Sphere where there are two reflections from the mirror surface under test (c.f. Equations 4 and 5).

From the foregoing it will be appreciated that the convex mirror testing method of the present invention employs smaller diameter and less expensive ancillary optical components. The method further provides a null testing method that may be set up at convenient conjugate distances. 

The invention claimed is:
 1. A method for producing a convex mirror having a desired surface quality wherein the mirror under test, the test optic, is treated as a lens prior to applying a reflective coating to the convex surface of the test optic substrate comprising the steps of: a) choosing an optical lens quality material for the test optic substrate, the test optic having a front convex surface side and a rear side; b) polishing the rear side of the test optic to a precise surface figure, thereby transforming the test optic into a lens; c) iteratively testing and polishing the test optic until a desired convex surface quality is obtained using a standard interferometric or wavefront lens-testing method; and d) once the desired convex surface is obtained, coating the convex surface with a reflective material to thereby produce a desired convex mirror.
 2. The method of claim 1, wherein the precise surface figure of the rear side of the test optic is an optical flat.
 3. The method of claim 1, wherein the precise surface figure of the rear side of the test optic is a spherical convex or concave shape, or an aspheric convex or concave shape.
 4. A null-testing method for determining the optical surface quality of a convex mirror wherein the mirror under test, the test optic, is treated as a lens prior to applying a reflective coating to the convex surface of the test optic substrate comprising the steps of: a) choosing an optical lens quality material for the test optic substrate, the test optic having a front convex surface side and a rear side, the desired convex surface having in general an aspherical curvature that introdubes a spherical aberration that can be pre-calculated when tested at conjugates other than those intended in its final application; b) polishing the rear side of the test optic to a precise optical surface, thereby transforming the test optic into a lens; c) passing a collimated beam from an interferometer through a focusing lens designed to introduce an equal and opposite amount of spherical aberration to that calculated for the desired test optic and to fill the test optic lens with the interferometer beam, through both front and rear surfaces of the test optic, being reflected back from a return mirror, back through both surfaces of the test optic, and then back through the focusing lens to form a null interference pattern if the test optic has the desired convex surface.
 5. A method for testing the optical surface quality of a convex mirror, the test optic, wherein the test optic is first transformed into a lens and tested prior to applying a reflective coating to the convex surface of the test optic substrate comprising the steps of: a) choosing an optical lens quality material for the test optic substrate, the test optic having a front convex surface side and a rear side; b) polishing the rear side of the test optic to a precise optical flat surface, thereby transforming the test optic into a lens with the rear optical fiat surface acting as a return mirror, c) passing a collimated beam from an interferometer through a transmission sphere producing near-perfect spherical wavefronts that pass through the front surface of the test optic, are partially reflected back from the rear optical flat surface, pass back through the front surface of the test optic, and then back through the transmission sphere to produce a wavefront error measurement of the front convex surface; d) determining the test optic convex surface error by subtracting a predicted wavefront error based on a desired test optic convex surface from the measured wavefront error, e) iteratively testing and polishing the test optic until a desired convex surface quality is obtained using steps c) and d); and f) once the desired convex surface is obtained, coating the convex surface with a reflective material to thereby produce a desired convex mirror.
 6. A method for testing the optical surface quality of a convex mirror, the test optic, wherein the test optic is first transformed into a lens and tested prior to applying a reflective coating to the convex surface of the test optic substrate comprising the steps of: a) choosing an optical lens quality material for the test optic substrate, the test optic having a front convex surface and a rear side; b) polishing the rear side of the test optic to a precise optical flat surface; c) passing a collimated beam from an interferometer through a focusing lens that initially converges then diverges said beam; d) locating the test optic at a position where said diverging beam fills the test optic lens so that said beam then passes through both front and rear surface of the test optic, is reflected back from a return minor, back through both surfaces of the test optic, and then back through the focusing lens creating a fringe pattern produced by any irregularities in the convex surface under test; e) determining the test optic convex surface error from said fringe pattern; f) iteratively testing and polishing the test optic until a desired convex surface quality is obtained, and g) once the desired convex surface is obtained, coating the convex surface with a reflective material to thereby produce a desired convex minor. 